LaTex数学公式(二)常用符号

1、希腊字母

语法显示语法显示
\alpha\(\alpha\)\beta\(\beta\)
\gamma\(\gamma\)\delta\(\delta\)
\epsilon\(\epsilon\)\zeta\(\zeta\)
\eta\(\eta\)\theta\(\theta\)
\iota\(\iota\)\kappa\(\kappa\)
\lambda\(\lambda\)\mu\(\mu\)
\nu\(\nu\)\xi\(\xi\)
\pi\(\pi\)\rho\(\rho\)
\sigma\(\sigma\)\tau\(\tau\)
\upsilon\(\upsilon\)\phi\(\phi\)
\chi\(\chi\)\psi\(\psi\)
\omega\(\omega\)

另外,每个希腊字母都有小写大写斜体三种显示格式。以π为例:

语法显示语法显示语法显示
\pi\(\pi\)\Pi\(\Pi\)\varPi\(\varPi\)

2、运算符

语法显示
x + y\(x + y\)
x \oplus y\(x \oplus y\)
x - y\(x -y\)
x \ominus y\(x \ominus y\)
x \times y\( x \times y\)
x \otimes y\(x \otimes y\)
x \bigotimes y\(x \bigotimes y\)
x \cdot y\( x \cdot y\)
x \odot y\(x \odot y\)
x \bigodot y\(x \bigodot y\)
x \ast y
x * y
\( x * y\)
x \star y\(x \star y\)
x \div y\( x \div y\)
x \pm y
x \mp y
\(x \pm y\)
\(x \mp y\)
x = y\(x = y\)
x \neq y\( x \neq y\)
x < y\(x < y\)
x \nless y\(x \nless y\)
x > y\(x > y\)
x \ngtr y\(x \ngtr y\)
x \leq y\(x \leq y\)
x \nleqslant y\(x \nleqslant y\)
x \geq y\(x \geq y\)
x \ngeqslant y\(x \ngeqslant y\)
x \ll y\(x \ll y\)
x \gg y\(x \gg y\)
x \doteq y\(x \doteq y\)
x \sim y\(x \sim y\)
x \not\sim y\(x \not\sim y\)
x \simeq y\(x \simeq y\)
x \not\simeq y\(x \not\simeq y\)
x \approx y\(x \approx y\)
x \not\approx y\(x \not\approx y\)
x \asymp y\(x \asymp y\)
x \not\asymp y\(x \not\asymp y\)
x \cong y\(x \cong y\)
x \not\cong y\(x \not\cong y\)
x \equiv y\(x \equiv y\)
x \not\equiv y\(x \not\equiv y\)

集合运算符:

语法显示
x \in y\(x \in y\)
x \notin y\(x \notin y\)
x \ni y\(x \ni y\)
x \not\ni y\(x \not\ni y\)
x \subset y\(x \subset y\)
x \subseteq y\(x \subseteq y\)
x \sqsubset y\(x \sqsubset y\)
x \sqsubseteq y\(x \sqsubseteq y\)
x \not\sqsubset y\(x \not\sqsubset y\)
x \not\sqsubseteq y\(x \not\sqsubseteq y\)
x \not\subset y\(x \not\subset y\)
x \not\subseteq y\(x \not\subseteq y\)
x \subsetneqq y\(x \subsetneqq y\)
x \supset y\(x \supset y\)
x \supseteq\(x \supseteq y\)
x \sqsupset y\(x \sqsupset y\)
x \sqsupseteq y\(x \sqsupseteq y\)
x \not\sqsupseteq y\(x \not\sqsupseteq y\)
x \not\sqsupset y\(x \not\sqsupset y\)
x \not\supseteq y\(x \not\supseteq y\)
x \not\supseteq y\(x \not\supseteq y\)
x \supsetneqq y\(x \supsetneqq y\)
x \cup y\(x \cup y\)
x \cap y\(x \cap y\)
\emptyset\(\emptyset\)
\varnothing\(\varnothing\)

3、上下标

语法显示
_ 和 ^\({a_n}^2\)
\vec\(\vec a\)
\(\vec {ab}\)
\overightarrow\(\overrightarrow a\)
\(\overrightarrow {ab}\)
\hat\(\hat a\)
\overline\(\overline a\)
\underline\(\underline a\)
\overbrace\(\overbrace{a+b}^{2.0}\)
\underbrace\(\underbrace{a+b}_{2.0}\)

4、箭头

单向箭头:

语法显示
\uparrow\(\uparrow\)
\Uparrow\(\Uparrow\)
\upharpoonleft\(\upharpoonleft\)
\upharpoonright\(\upharpoonright\)
\upuparrows\(\upuparrows\)
\downarrow\(\downarrow\)
\Downarrow\(\Downarrow\)
\downharpoonleft\(\downharpoonleft\)
\downharpoonright\(\downharpoonright\)
\downdownarrows\(\downdownarrows\)
\leftarrow\(\leftarrow\)
\Leftarrow\(\Leftarrow\)
\longleftarrow\(\longleftarrow\)
\Longleftarrow\(\Longleftarrow\)
\leftharpoonup\(\leftharpoonup\)
\leftharpoondown\(\leftharpoondown\)
\leftleftarrows\(\leftleftarrows\)
\rightarrow\(\rightarrow\)
\Rightarrow\(\Rightarrow\)
\longrightarrow\(\longrightarrow\)
\Longrightarrow\(\Longrightarrow\)
\rightharpoonup\(\rightharpoonup\)
\rightharpoondown\(\rightharpoondown\)
\rightrightarrows\(\rightrightarrows\)

双向箭头:

语法显示
\leftrightarrow\(\leftrightarrow\)
\Leftrightarrow\(\Leftrightarrow\)
\longleftrightarrow\(\longleftrightarrow\)
\Longleftrightarrow\(\Longleftrightarrow\)
\updownarrow\(\updownarrow\)
\Updownarrow\(\Updownarrow\)
\rightleftharpoons\(\rightleftharpoons\)
\leftrightharpoons\(\leftrightharpoons\)

其他箭头:

语法显示
\swarrow\(\swarrow\)
\nearrow\(\nearrow\)
\nwarrow\(\nwarrow\)
\searrow\(\searrow\)

5、字体

字体语法显示
默认\ {A}\(\ {ABCDEFG}\)
等线体\sf{A}\(\sf{ABCDEFG}\)
打印机体\tt {A}\(\tt {ABCDEFG}\)
罗马体\rm {A}\(\rm {ABCDEFG}\)
宋体\bf {A}\(\bf {ABCDEFG}\)
黑板粗体\Bbb{A}\(\Bbb{ABCDEFG}\)
意大利体\it{A}\(\it{ABCDEFG}\)
德文字体\frak{A}\(\frak{ABCDEFG}\)

6、空白和省略

说明语法显示
ab\(ab\)
空格(Space)a\ b\(a\ b\)
4个空格(Tab)a\quad b\(a\quad b\)
省略号(下)1,2,\ldots,n\(1,2,\ldots,n\)
省略号(中)x_1^2 + x_2^2 + \cdots + x_n^2\(x_1^2 + x_2^2 + \cdots + x_n^2\)

7、矩阵

说明语法显示
基本\begin{matrix}1&0&0\\0&1&0\\0&0&1\\\end{matrix}\(\begin{matrix}1&0&0\\0&1&0\\0&0&1\\\end{matrix}\)
小括号边框\begin{pmatrix}1&0&0\\0&1&0\\0&0&1\\\end{pmatrix}\(\begin{pmatrix}1&0&0\\0&1&0\\0&0&1\\\end{pmatrix}\)
中括号边框\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\\\end{bmatrix}\(\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\\\end{bmatrix}\)
大括号边框\begin{Bmatrix}1&0&0\\0&1&0\\0&0&1\\\end{Bmatrix}\(\begin{Bmatrix}1&0&0\\0&1&0\\0&0&1\\\end{Bmatrix}\)
单竖线边框\begin{vmatrix}1&0&0\\0&1&0\\0&0&1\\\end{vmatrix}\(\begin{vmatrix}1&0&0\\0&1&0\\0&0&1\\\end{vmatrix}\)
双竖线边框\begin{Vmatrix}1&0&0\\0&1&0\\0&0&1\\\end{Vmatrix}\(\begin{Vmatrix}1&0&0\\0&1&0\\0&0&1\\\end{Vmatrix}\)

此外,矩阵中还能使用省略号。

  • 横省略号:\cdots( \(\cdots\))
  • 竖省略号:\vdots( \(\vdots\))
  • 斜省略号:\ddots( \(\ddots\))

例:

LaTeX
1
2
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$$\begin{bmatrix}
{a_{11}}&{a_{12}}&{\cdots}&{a_{1n}}\\
{a_{21}}&{a_{22}}&{\cdots}&{a_{2n}}\\
{\vdots}&{\vdots}&{\ddots}&{\vdots}\\
{a_{m1}}&{a_{m2}}&{\cdots}&{a_{mn}}\\
\end{bmatrix}$$

效果如下:

$$\begin{bmatrix}
{a_{11}}&{a_{12}}&{\cdots}&{a_{1n}}\\
{a_{21}}&{a_{22}}&{\cdots}&{a_{2n}}\\
{\vdots}&{\vdots}&{\ddots}&{\vdots}\\
{a_{m1}}&{a_{m2}}&{\cdots}&{a_{mn}}\\\end{bmatrix}$$

8、阵列

基本语法:

  • 起始结束:{array}
  • 对齐声明

    • 左对齐:l
    • 居中:c
    • 右对齐:r
  • 水平线: \hline

例:

LaTeX
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$$\begin{array}{c|lll}
{↓}&{a}&{b}&{c}\\
\hline
{R_1}&{c}&{b}&{a}\\
{R_2}&{b}&{c}&{c}\\
\end{array}$$

效果如下:

$$\begin{array}{c|lll}
{↓}&{a}&{b}&{c}\\
\hline
{R_1}&{c}&{b}&{a}\\
{R_2}&{b}&{c}&{c}\\
\end{array}$$

9、方程组

声明:{cases}

例:

LaTeX
1
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$$\begin{cases}
a_1x+b_1y+c_1z=d_1\\
a_2x+b_2y+c_2z=d_2\\
a_3x+b_3y+c_3z=d_3\\
\end{cases}
$$

效果如下:

$$\begin{cases}
a_1x+b_1y+c_1z=d_1\\
a_2x+b_2y+c_2z=d_2\\
a_3x+b_3y+c_3z=d_3\\
\end{cases}$$

10、函数

语法显示语法显示
\sin\theta\(\sin \theta\)\cos\theta\(\cos \theta\)
\arcsin\frac{L}{r}\(\arcsin\frac{L}{r}\)\arccos\frac{T}{r}\(\arccos\frac{T}{r}\)
\sinh g\(\sinh g\)\cosh h\(\cosh h\)
\operatorname{sh}j\(\operatorname{sh}j\)\operatorname{argsh}k\(\operatorname{argsh}k\)
\operatorname{argch}l\(\operatorname{argch}l\)\operatorname{th}i\(\operatorname{th}i\)
k’(x)=\lim_{\Delta x\to 0}\frac{k(x)-k(x-\Delta x)}{\Deltax}\(k'(x)=\lim_{\Delta x\to0} \frac{k(x)-k(x-\Delta x)}{\Delta x}\)\limsup S\(\limsup S\)
\max H\(\max H\)\min L\(\min L\)
\sup t\(\sup t\)\exp t\(\exp t\)
\lg X\(\lg X\)\log X\(\log X\)
\ker x\(\ker x\)\deg x\(\deg x\)
\Pr x\(\Pr x\)\det x\(\det x\)
\arg x\(\arg x\)\dim x\(\dim x\)
\tan\theta\(\tan \theta\)\arctan\frac{L}{T}\(\arctan\frac{L}{T}\)
\tanh i\(\tanh i\)\operatorname{ch}h\(\operatorname{ch}h\)
\operatorname{argth}m\(\operatorname{argth}m\)\liminf I\(\liminf I\)
\inf s\(\inf s\)\ln X\(\ln X\)
\log_\alpha X\(\log_\alpha X\)\gcd(T,U,V,W,X)\(\gcd(T,U,V,W,X)\)
\hom x\(\hom x\)\lim_{t\to n}T\(\lim_{t\to n}T\)

微分与导数:

语法显示
dt\(dt\)
\mathrm{d}t\( \mathrm{d}t\)
\partial t\( \partial t\)
\nabla\psi\( \nabla\psi\)
dy/dx\(dy/dx\)
\mathrm{d}y/\mathrm{d}x\( \mathrm{d}y/\mathrm{d}x\)
\frac{dy}{dx}\( \frac{dy}{dx}\)
\frac{\mathrm{d}y}{\mathrm{d}x}\( \frac{\mathrm{d}y}{\mathrm{d}x}\)
\frac{\partial^2}{\partial x_1\partial x_2}y\( \frac{\partial^2}{\partial x_1\partial x_2}y\)
\prime\(\prime\)
\backprime\( \backprime\)
f^\prime\( f^\prime\)
f'\( f'\)
f''\( f''\)
f^{(3)}\( f^{(3)}\)
\dot y\( \dot y\)
\ddot y\( \ddot y\)

求和积、积分:

语法显示
\sum_{k=1}^N k^2\(\sum_{k=1}^N k^2\)
\begin{matrix} \sum_{k=1}^N k^2 \end{matrix}\(\begin{matrix} \sum_{k=1}^N k^2 \end{matrix}\)
\prod_{i=1}^N x_i\(\prod_{i=1}^N x_i\)
\begin{matrix} \prod_{i=1}^N x_i \end{matrix}\(\begin{matrix} \prod_{i=1}^N x_i \end{matrix}\)
\coprod_{i=1}^N x_i\(\coprod_{i=1}^N x_i\)
\begin{matrix} \coprod_{i=1}^N x_i \end{matrix}\(\begin{matrix} \coprod_{i=1}^N x_i \end{matrix}\)
\int_{-N}^{N} e^x\, {\rm d}x\(\int_{-N}^{N} e^x\, {\rm d}x\)
\begin{matrix} \int_{-N}^{N} e^x\, \mathrm{d}x \end{matrix}\(\begin{matrix} \int_{-N}^{N} e^x\, \mathrm{d}x \end{matrix}\)
\iint_{D}^{W} \, \mathrm{d}x\,\mathrm{d}y\(\iint_{D}^{W} \, \mathrm{d}x\,\mathrm{d}y\)
\iiint_{E}^{V} \, \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z\(\iiint_{E}^{V} \, \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z\)
\oint_{C} x^3\, \mathrm{d}x + 4y^2\, \mathrm{d}y\(\oint_{C} x^3\, \mathrm{d}x + 4y^2\, \mathrm{d}y\)

11、参考

LaTeX公式手册
https://www.cnblogs.com/1024th/p/11623258.html

LaTex数学公式(二)常用符号

https://blog.tsinbei.com/tw/archives/929/

文章作者
Hsukqi Lee
发布于

2022-11-08

修改于

2023-02-13

许可协议

CC BY-NC-ND 4.0

# 学习  LaTex

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